Q.Describe briefly:

(a) Arithmetic growth: after mitosis, only one daughter cell continues to divide while the other differentiates and matures; growth is at a constant rate and a plot of size against time gives a straight line (for example, a root elongating steadily). (b) Geometric growth: both daughter cells continue to divide, so the number of dividing cells increases exponentially; growth is slow initially (lag phase) and rapid later (log phase). (c) Sigmoid growth curve: the S-shaped curve obtained when growth over time is plotted, showing a lag phase, a rapid log (exponential) phase, and a stationary phase; it is typical of all cells, tissues and organs in a natural environment. (d) Absolute growth rate is the total growth per unit time; relative growth rate is the growth per unit time expressed per unit of the initial amount of material present.

1. Arithmetic growth In arithmetic growth, following mitotic cell division only one of the two daughter cells continues to divide, while the other differentiates and matures. As a result the growth rate is constant, and a plot of length (or size) against time gives a straight line. It can be expressed as Lt = L0 + rt, where Lt is length at time t, L0 is length at the start, and r is the growth rate per unit time. A classic example is a root or shoot elongating at a constant rate.
2. Geometric growth In geometric growth, both daughter cells produced by mitosis retain the ability to divide and continue to do so. Because the number of dividing cells keeps increasing, growth is exponential. It is typically slow in the beginning — the lag phase — followed by a period of rapid, exponential increase — the log or exponential phase. However, limited nutrient supply in a natural environment prevents this exponential growth from continuing indefinitely.
3. Sigmoid growth curve When growth is plotted against time for cells, tissues, organs or a whole organism in a natural setting, an S-shaped (sigmoid) curve is obtained. It has three phases: a lag phase (slow initial growth), a log/exponential phase (rapid growth), and a stationary phase (growth slows and levels off as resources become limiting). This sigmoid curve is characteristic of living cells growing in a natural environment.
4. Absolute and relative growth rates Absolute growth rate is the measurement and comparison of total growth per unit time. Relative growth rate is the growth of a system per unit time expressed on a common basis, i.e., per unit initial parameter. For example, two leaves A and B may each increase their area by the same 5 square centimetres in a given time, but because leaf A started smaller, its relative growth is greater even though the absolute increase is identical.
   ✓Final answer

   (a) Arithmetic growth = only one daughter cell keeps dividing, constant rate, straight-line graph. (b) Geometric growth = both daughter cells keep dividing, exponential (lag then log). (c) Sigmoid growth curve = the S-shaped curve of growth vs time with lag, log and stationary phases, typical in nature. (d) Absolute growth rate = total growth per unit time; relative growth rate = growth per unit time per unit of initial size.

Method: Classifying a Growth Pattern as Arithmetic, Geometric or Sigmoid, and Computing Growth Rates

Any question describing how a measurement changes over time is really asking you to recognise one of these three growth patterns, or to compute one of the two growth-rate formulas.

Steps

Step 1: Check whether the increase per unit time stays constant or itself grows.

If growth adds the same amount each interval (a straight-line plot), it is arithmetic growth: Lt = L0 + rt, where Lt is the size at time t, L0 is the starting size, and r is the constant growth rate. This happens when, after mitosis, only ONE daughter cell keeps dividing.

Step 2: If the increase itself accelerates, it is geometric growth.

Both daughter cells keep dividing, so the number of dividing units doubles each cycle — expressed as W1 = W0 x e^(rt), giving a slow lag phase followed by a fast log (exponential) phase. Recognise this pattern whenever a population or tissue is said to double or multiply repeatedly.

Step 3: If growth is plotted for a real organism over its full life, expect an S-shaped (sigmoid) curve.

Natural growth is geometric only briefly — limited nutrients eventually flatten it into a lag phase, a log phase, and a stationary phase. This three-phase S-curve is the default expectation for any real cell, tissue or organism growing in a natural environment.

Step 4: To compute a growth rate, always divide the change by something — absolute growth rate divides change by time; relative growth rate divides change by the starting value.

Absolute growth rate = (final size minus initial size) / time elapsed. Relative growth rate = (final size minus initial size) / initial size — this is what lets you fairly compare a small structure's growth against a large one's.